British fruit and vegetables would all but vanish from shops if Brexit means the foreign workers who pick virtually all the home-grown produce are no longer able to come to the UK, according to some of the country’s biggest producers.

They warn that the nation’s food security would be damaged and that produce in UK shops would become more expensive if the freedom of movement for EU workers came to an end. They are urging ministers to set up a new permit scheme for seasonal workers.

Without a scheme, they say production would move abroad, where many already have large operations, or would switch to cereals which are harvested by machines. The Brexit vote is already deterring foreign workers from coming to the UK, the producers report.

About 90% of British fruit, vegetables and salads are picked, graded and packed by 60,000 to 70,000 workers from overseas, mostly from eastern Europe. Many of these work in areas which voted very strongly to leave the EU: the largely agricultural borough of Boston in Lincolnshire had the highest vote for leaving the EU in the whole country, at 75%.

“If we don’t have freedom of movement and they don’t replace it with a permit scheme then the industry will just close down” in the UK, said John Shropshire, chairman of G’s, one of the nation’s biggest producers of salads and vegetables, which employs 2,500 seasonal workers and also has farms in Spain, Poland, the Czech Republic and Senegal. “No British person wants a seasonal job working in the fields. They want permanent jobs or jobs that are not quite as taxing physically.”

“The government has to make a decision: either we bring the people to the work or we take the work to the people,” he told the Guardian. “The government has to decide does it want [the UK] to produce food or not - that is their decision.”

Angus Davison, chairman at Haygrove, a major berry and cherry producer, employing 800 seasonal workers, said that without them their growing would be exported: “We would move it to the continent. We wouldn’t be able to operate here in the UK because we would not be able to harvest the crops.” Half of Haygrove’s production is already in Portugal and South Africa.

“Do you want all your fresh produce to come from foreign countries?” he asked. “There would be more risks around its security, we wouldn’t be as food secure as a nation.” Davison said his company had 15 workers a day applying to its offices in Romania and Bulgaria before the Brexit referendum, but this has dropped now to one or two: “We are genuinely concerned. People over there are feeling they are not wanted here.”

More than 98% of those coming to the UK through a previous Seasonal Agricultural Workers scheme returned home. It ran from 1948 to 2013, when Theresa May as home secretary scrapped it. Davison said: “Seasonal workers for harvesting crops are not migrants. They come here to do a job and they go away again.” Davison and other producers told the Guardian their existing seasonal staff had been very unsettled by the Brexit vote and that there was a moral duty for the government to clarify their future status.

The UK produces only half of the fresh produce it eats, but despite consumers wanting more British-grown fruit, vegetables and salad, the investment to increase the nation’s self-sufficiency is at risk if seasonal workers are not available, said Chris Mack, chairman at Fresca Group, another major producer whose businesses include five huge salad greenhouses at Thanet in Kent, where 64% of voters backed leaving the EU.

“We were hoping to build the sixth [greenhouse], but unless we have the people to go and pick the tomatoes, it’s difficult to see how we are going to do that,” he said. The introduction of the national living wage was already causing fruit and vegetable producers, who do not receive EU subsidies, to move to lower cost countries, Mack said: “If there is a further issue around the availability of labour, moving your fields overseas will be almost be the only option.”

Mack also said shoppers will be hit in the pocket if Brexit negotiations lead to no freedom of movement and no access to the single EU market: “There will be less access to fresh produce and prices will inevitably then go up.”

It is not just major producers who are concerned about the availability of seasonal workers. Erica Consterdine, from the University of Sussex’s Centre for Migration Research, said: “What is absolutely certain is that, without foreign labour, there are going to be massive labour market shortages. I’m not sure the government quite realises just how reliant these sectors are on EU labour.”

“It’s looking pretty bad in terms of the security of the food supply chain. It would be disastrous,” she said. “I can’t really see how the industry can survive in the long term without freedom of movement of workers, without reintroducing some kind of agricultural workers scheme. Economically, looking at the sector, it seems absolutely crazy not to.”

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A government spokesperson said: “Nothing is changing overnight – freedom of movement remains in place while we are in the EU. The public clearly demanded control over immigration in the EU referendum and that is what we are going to deliver, but it will take some time. There will clearly be challenges to overcome in our negotiations to leave the EU, but Brexit means Brexit and we’re going to make a success of it.”

The National Farmers Union (NFU) is undertaking its largest ever consultation with its members after Brexit, with the issue of seasonal labour a key element. “There is a huge threat to an extremely important sector of British farming,” said Meurig Raymond, NFU president. “How often did we hear from the leave campaigners that we wanted to see more controlled immigration? The seasonal workers scheme was a controlled system.”

Attempts to recruit British workers for seasonal work have failed, farmers told the Guardian. Those willing to take temporary jobs opt for hospitality and other sectors, while others sent by unemployment offices rarely last a week, they said.

“I know one or two companies that have gone to very significant lengths to set up a supply of UK labour and it just hasn’t worked,” said Jack Ward, chief executive of the British Growers Association. “I think it is probably the outdoor nature of the work.” Consterdine said a pilot scheme from the Department of Work and Pensions had been “totally unsuccessful”.

The fresh produce industry is not the only farming sector warning of the risks of losing migrant workers. “If the central and eastern Europeans went back to their native countries then dairy farming would be in dire straits,” said Tim Brigstocke, policy director at the Royal Association of British Dairy Farmers.

Roger Kelsey, a former butcher and now chief executive of the National Federation of Meat & Food Traders, said the UK meat industry was heavily reliant on labour from overseas: “It would not survive without them. Go into any abattoir or meat processing factory in the east of England – or anywhere in the UK – and you will see Polish and Portuguese workers helping the slaughtermen and doing what are seen as the unpleasant jobs, such as evisceration.” Even the vets employed by the Food Standards Agency are overwhelmingly - 98% - from the from EU nations.

All these sectors supply the UK’s biggest manufacturing sector: food and drink. The Food and Drink Federation (FDF) says its 7,000 member businesses employ 130,000 people from eastern Europe – more than a quarter of entire workforce. “If we are to remain competitive, we need urgent reassurance for the EU nationals working in the UK food and drink manufacturing sector and continuing unhindered access to workers from the EU,” said Ian Wright, FDF director general recently.

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John Hardman, at the agricultural employment agency HOPS Labour Solutions, told the Farmers Guardian he was not optimistic that avoiding the loss of seasonal workers was high in government priorities: “We may only just start to move up that list when we cannot pick all of the strawberries for Wimbledon or Brussels sprouts for Christmas.”

Shropshire is more confident however: “I just can’t believe it will happen. “It would be a great shame for the country to export a large chunk of the British fresh produce industry.”

Laurence Olins, chairman of industry group British Summer Fruits, recently sent a letter and a large tray of fresh strawberries, raspberries and other berries to the new environment and home secretaries, Andrea Leadsom and Amber Rudd: “I sent the tray so they could actually taste them and see what they would be missing.”